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Thread: inequality in quadrilateral

  1. #1
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    inequality in quadrilateral

    In convex quadrilateral ABCD, K is midpoint of AB, M is midpoint CD,. Prove that $ KM \le \frac{BC+AD}{2} $.
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  2. #2
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    Quote Originally Posted by olkaabc View Post
    Prove that $ KM \le \frac{BC+AD}{2} $.
    Huh?
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  3. #3
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    Quote Originally Posted by olkaabc View Post
    In convex quadrilateral ABCD, K is midpoint of AB, M is midpoint CD,. Prove that $\displaystyle KM \le \frac{BC+AD}{2} $.
    We know that $\displaystyle \frac{1}{2}\overrightarrow {AB} + \overrightarrow {BC} + \frac{1}{2}\overrightarrow {CD} = \overrightarrow {KM} $ and $\displaystyle -\frac{1}{2}\overrightarrow {AB} + \overrightarrow {AD} - \frac{1}{2}\overrightarrow {CD} = \overrightarrow {KM} $

    If you add those two together and divide by two, what do get?
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